Sobolev inequalities with symmetry

In this paper we derive some Sobolev inequalities for radially symmetric functions in ˙H s with 1 2 < s < n 2 . We show the end point case s = 1 2 on the homogeneous Besov space ˙B 12 2;1. These results are extensions of the well-known Strauss’ inequality [11]. Also non-radial extensions are given, which show that compact embeddings are possible in some Lp spaces if a suitable angular regularity is imposed